Extended Gaussian images, mixed volumes, shape reconstruction
Proceedings of the first annual symposium on Computational geometry, page 15--23. New York, NY, USA, ACM, (1985)DOI: 10.1145/323233.323236
Abstract
The Extended Gaussian Image (EGI) of an object records the variation of surface area with surface orientation. The EGI is a unique representation for convex objects. For a polyhedron, each face is represented by its normal and its area. The inversion problem (from an EGI to a description in terms of vertices and faces) is solved for convex polyhedra, by providing an algorithm giving an iterative solution by a minimizationLittle,1983. The algorithm employs a geometric construction, the mixed volume, which was used in Minkowski's proof 1897 of the existence and uniqueness of an inverse. The mixed volume measures similarity of shape for convex objects.
